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International Conference on Evolutionary Multi-Criterion Optimization

EMO 2011: Evolutionary Multi-Criterion Optimization pp 313–327Cite as

A Bi-objective Based Hybrid Evolutionary-Classical Algorithm for Handling Equality Constraints

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6576))

Abstract

Equality constraints are difficult to handle by any optimization algorithm, including evolutionary methods. Much of the existing studies have concentrated on handling inequality constraints. Such methods may or may not work well in handling equality constraints. The presence of equality constraints in an optimization problem decreases the feasible region significantly. In this paper, we borrow our existing hybrid evolutionary-cum-classical approach developed for inequality constraints and modify it to be suitable for handling equality constraints. This modified hybrid approach uses an evolutionary multi-objective optimization (EMO) algorithm to find a trade-off frontier in terms of minimizing the objective function and the constraint violation. A suitable penalty parameter is obtained from the frontier and then used to form a penalized objective function. The procedure is repeated after a few generations for the hybrid procedure to adaptively find the constrained minimum. Unlike other equality constraint handling methods, our proposed procedure does not require the equality constraints to be transformed into an inequality constraint. We validate the efficiency of our method on six problems with only equality constraints and two problems with mixed equality and inequality constraints.

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Author information

Authors and Affiliations

  1. Kanpur Genetic Algorithms Laboratory (KanGAL), Department of Mechanical Engineering, Indian Institute of Technology Kanpur, 208016, India

    Rituparna Datta & Kalyanmoy Deb

Authors
  1. Rituparna Datta
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  2. Kalyanmoy Deb
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Editor information

Editors and Affiliations

  1. Department of Mathematics, Federal University of Minas Gerais, Av. Antônio Carlos 6627, 31270-901, Belo Horizonte, MG, Brazil

    Ricardo H. C. Takahashi

  2. Department of Mechanical Engineering, Indian Institute of Technology Kanpur, 208 016, Kanpur, India

    Kalyanmoy Deb

  3. Department of Computer Engineering, Centro Federal de Educaçao Tecnológica de Minas Gerais, Av. Amazonas 5253, 30421-169, Belo Horizonte, MG, Brazil

    Elizabeth F. Wanner

  4. Faculty of Economics, University of Catania, Corso Italia 55, 95129, Catania, Italy

    Salvatore Greco

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© 2011 Springer-Verlag Berlin Heidelberg

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Datta, R., Deb, K. (2011). A Bi-objective Based Hybrid Evolutionary-Classical Algorithm for Handling Equality Constraints. In: Takahashi, R.H.C., Deb, K., Wanner, E.F., Greco, S. (eds) Evolutionary Multi-Criterion Optimization. EMO 2011. Lecture Notes in Computer Science, vol 6576. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-19893-9_22

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  • DOI: https://doi.org/10.1007/978-3-642-19893-9_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-19892-2

  • Online ISBN: 978-3-642-19893-9

  • eBook Packages: Computer ScienceComputer Science (R0)

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